The present invention relates to bulk acoustic wave filters (also known as BAW filters) that are constructed according to the reactance filter principle.
From an article by K. M. Lakin et al. in Microwave Symposium Digest, IEEE MTT-S International 1995, pp. 883–886, it is known to construct reactance filters from BAW resonators. Here, these resonators are used as impedance elements, and are for example wired or connected to form ladder-type or lattice filters. This type of wiring for the manufacture of filters is also known as branching technology.
According to FIG. 1a, in its simplest specific embodiment a BAW resonator R is made up of a thin film P of a piezoelectric material, which is provided with an electrode E1, E2 on its upper and lower side respectively. Ideally, this structure is surrounded by air on both electrode sides. When an electrical voltage is applied to the electrodes, an electrical field acts on the piezoelectric layer, with the result that the piezoelectric material converts a part of the electrical energy into mechanical energy in the form of acoustic waves. These waves propagate parallel to the field direction, as what are known as bulk waves, and are reflected at the electrode/air boundary surfaces. At a particular frequency fr, which is dependent on the thickness of the piezoelectric layer or on the thickness of the bulk resonator, the resonator exhibits a resonance, and thus behaves like an electrical resonator.
In the equivalent circuit diagram according to FIG. 1b, the BAW resonator R is made up of a series resonance circuit of dynamic inductance L1, dynamic capacitance C1, and dynamic resistance R1, as well as a static capacitance C0, connected thereto in parallel. The series resonance circuit reproduces the behavior of the resonator in the resonance case, i.e., in the range of resonance frequency fr. Static capacitance C0 reproduces the behavior in the range f<<fr and fr>>f. Dynamic capacitance C1 is thereby proportional to the static capacitance C0 of the BAW resonator.C1˜C0.  (1.1)For the resonance frequency fr and the anti-resonance frequency fa of a BAW resonator, the following hold:
                              f          r                =                              1                          2              ⁢              π              ⁢                                                L1                  ·                  C1                                                              ⁢                                          ⁢          and                                    (        1.2        )                                          f          a                =                              f            r                    ⁢                                                    1                +                                  C1                  C0                                                      .                                              (        1.3        )            
According to FIG. 7, a reactance filter is made up of at least one basic element that has a serially connected resonator R2 having a resonance frequency frs and an associated anti-resonance frequency fas, and that has a second resonator R1 that is connected parallel to a second terminal, in particular parallel to ground, having a resonance frequency frp and an associated anti-resonance frequency fap. In order to produce a filter having a bandpass characteristic and a center frequency f0, the following relation holds for the two resonators in the serial or in the parallel branch:fap≈frs≈f0  (1.4).
FIG. 16a shows the curve of the impedance Zs of the serial resonator and of the admittance Yp of the parallel resonator, plotted over the frequency f. FIG. 16b shows the passband response of a filter made up of a basic element, whose resonance frequencies are selected as in FIG. 16a. FIG. 7 shows a basic element that is to be regarded in principle as a two-port network having terminals 3-1 or 3-2 as a port 1 and having terminals 3-3 or 3-4 as a port 2. At the same time, terminal 3-1 is the input and terminal 3-3 is the output of the series resonator. The input of the parallel resonator is connected with terminal 3-1. Terminals 3-2 and 3-4 represent the reference ground, given asymmetrical operation. The output 3-5 of parallel resonator R1, which faces the reference ground, is designated in the following as the output or ground side of the parallel resonator. The inductance Lser, which is situated between the output side of the parallel resonator and the reference ground, reflects the connection to the housing ground in the real construction.
The selection level of a reactance filter constructed from BAW resonators is determined on the one hand by the ratio C0p/C0s of the static capacitance COP in the parallel branch and the static capacitance C0s in the series branch, and on the other hand by the number of basic elements that are cascaded, i.e., connected in series with one another.
A plurality of basic elements can be wired together in matched fashion, whereby the structure of each of the second adjacent basic elements is mirrored. The output impedance of the first basic element (7-1 in FIG. 2, or 8-1 in FIG. 3) is then equal to the input impedance of the second basic element (7-2 in FIG. 2 or 8-2 in FIG. 3), so that only minimal losses are produced by mismatching. Many structures are known for the wiring of a plurality of basic elements. Some examples are shown in FIGS. 4 and 5.
Resonators of the same type (series resonators or parallel resonators) that are situated immediately one after the other in a circuit of a reactance filter can also be respectively combined to form a resonator, whereby the overall capacitive effect of the combined resonator remains constant.
From equations (1.2) to (1.4), it can be seen that both the maximum achievable bandwidth and also the steepness of the edges of such a reactance filter depend on the difference of the resonance and anti-resonance frequencies of the individual resonators. This difference in turn results from the ratio of dynamic capacitance C1 and static capacitance C0. Because these capacitances are proportional to one another, the capacitance ratio C1/C0 does not change when one of these capacitances is altered. For example, C0 could be varied by changing the size of the resonator. As a rule, all resonators of a reactance filter have the same relative bandwidth(fa−fr)/f0.
Curve 1 in FIG. 6 shows the passband response of a reactance filter that is constructed from uniform BAW resonators, with each resonator having a relatively large ratio of dynamic to static capacitance. The individual resonators thus have a relatively large bandwidth. Curve 2 is the passband curve of a corresponding reactance filter made up of resonators having a small ratio of dynamic to static capacitance, and thus a relatively low bandwidth of the individual resonators. In the first case (curve 1), a bandpass filter is obtained having a high bandwidth and a low edge steepness, while in the second case (curve 2) a bandpass filter is obtained having a low bandwidth and a high edge steepness.
If it is now attempted, in such a steep-edged filter, to increase the bandwidth to the level of the filter having the larger capacitance ratio by increasing the center frequencies of series resonators and/or reducing the center frequency of the parallel resonators, a strong mismatching results in the center of the passband, because now fap<<frs. Condition (1.4) is thus no longer fulfilled. For this reason, the losses in the center of the passband also increase more strongly.
Another possibility for broadening a steep-edged filter consists in a reduction of the ratio (C0p/C0s) of the static capacitance C0p in the parallel branch and the static capacitance C0s in the series branch. In this way, the bandwidth can be enlarged to a certain extent without losing the self-matching and the small losses connected therewith. However, with this measure the selection level of the BAW reactance filter is strongly reduced, so that the filter can no longer meet possible selection demands, and can for example no longer sufficiently attenuate undesired frequencies.